Finding intervals of increasing, decreasing, concavity and inflection points

[ryan.1015]

Homework Statement

let g(x)=2x^5-10x^3=15x-3. find the intervals on which G is increasing and decreasing. and find the intervals of concavity and the inflection points

Homework Equations

The Attempt at a Solution

i know how to find the increasing and decreasing intervals. i just can't figure out where the graphs cross the x axis. and the concavity intervals i can't figure out

 

[Mark44]

Show us what you've done...

 

[ryan.1015]

well i found the derivative to be 10x^4 +30x^2+15 but when i graphed it i couldt figure out where it crossed the x axis

 

[Mark44]

well i found the derivative to be 10x^4 +30x^2+15 but when i graphed it i couldt figure out where it crossed the x axis

Here's what you showed in your first post:

g(x)=2x^5-10x^3=15x-3.

What's with that '=' right after the x^3 term? Did you mean that to be a '+'?

Assuming that's the case, g(x) = 2x^5 - 10x^3 + 15x -3
Your calculation for the derivative -- g'(x) is its name -- is incorrect.

 

[ElectroPhysics]

I think from equating first derivative to zero u can easily find the point where no change occurs and beyond that it go on changing. and from 2nd derivative u can find the inflection points. Am I correct?

 

[Mark44]

I think from equating first derivative to zero u can easily find the point where no change occurs and beyond that it go on changing. and from 2nd derivative u can find the inflection points. Am I correct?

Equating the derivative to zero gives you the values where the tangent lines are horizontal, which can help you find local maxima and minima.